Question

Suppose the numbers of a particular type of bacteria in samples of 1 milliliter (ml) of drinking water tend to be approximately normally distributed, with a mean of 84 and a standard deviation of 8. What is the probability that a given 1 ml sample will contain more than 107 bacteria? (Round your answer to four decimal places.)

Answer 1

The probability that a given 1 ml sample will contain more than 107 bacteria is approximately 0.0022.

Step-by-step explanation:

To find the probability that a given 1 ml sample will contain more than 107 bacteria, we need to calculate the z-score and use the standard normal distribution table.

First, we calculate the z-score:

z = (x - mean) / standard deviation

z = (107 - 84) / 8 = 2.875

Next, we use the standard normal distribution table to find the probability of a z-score greater than 2.875. The closest value we can find is 0.9978.

Therefore, the probability that a given 1 ml sample will contain more than 107 bacteria is approximately 0.0022.